Calculus Examples

$\frac{lim_{x \to o} 6 x - 9}{x^{2} - 12 x - 3}$

Step 1

Evaluate the limit.

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Step 1.1

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $o$ .

$\frac{lim_{x \to o} 6 x - lim_{x \to o} 9}{x^{2} - 12 x - 3}$

Step 1.2

Move the term $6$ outside of the limit because it is constant with respect to $x$ .

$\frac{6 lim_{x \to o} x - lim_{x \to o} 9}{x^{2} - 12 x - 3}$

Step 1.3

Evaluate the limit of $9$ which is constant as $x$ approaches $o$ .

$\frac{6 lim_{x \to o} x - 1 \cdot 9}{x^{2} - 12 x - 3}$

Step 2

Evaluate the limit of $x$ by plugging in $o$ for $x$ .

$\frac{6 o - 1 \cdot 9}{x^{2} - 12 x - 3}$

Step 3

Simplify the numerator.

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Step 3.1

Multiply $- 1$ by $9$ .

$\frac{6 o - 9}{x^{2} - 12 x - 3}$

Step 3.2

Factor $3$ out of $6 o - 9$ .

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Step 3.2.1

Factor $3$ out of $6 o$ .

$\frac{3 (2 o) - 9}{x^{2} - 12 x - 3}$

Step 3.2.2

Factor $3$ out of $- 9$ .

$\frac{3 (2 o) + 3 (- 3)}{x^{2} - 12 x - 3}$

Step 3.2.3

Factor $3$ out of $3 (2 o) + 3 (- 3)$ .

$\frac{3 (2 o - 3)}{x^{2} - 12 x - 3}$